Answer :
Answer:
a) This is a permutation, there are 210 ways to do it
b) This is a permutation with 6 possibilities
c) This is a combination with a total of 1081575 possibilities
Step-by-step explanation:
a) Here the order does matter bacause it is not the same that they go to France in the weak trip than they go there for 2 days, as a result, this scenario is a permutation.
You need to pick 3 countries from a total of 7, but the order matters, so the total amount of ways to do this is
[tex] {7 \choose 3} * 3! = \frac{7!}{(7-3)!} = 210 [/tex]
b) Here each permutation of 123 will give you a possible (and a different one from the others) lock-combination, so this is again a permutation.
The total amount of ways we have to do the selectio of the lock-combination is the total amount of permutations of a set of 3 elements, in other words, it is 3! = 6.
c) If you only cares about who advances to the finals, then the order doesnt matter here, you just want 8 people out of the 25 available. This is therefore a combination, and the total amount of possible cases are
[tex] {25 \choos 8} = 1081575 [/tex] .
a. The number of possibilities that Castel and Joe are planning trips is [tex]35[/tex]
b. The number of possibilities of arranging three digit number is,6
c. The number of possibilities are [tex]1081575[/tex].
Permutation and combination :
a. We have to find the number of possibilities that Castel and Joe are planning trips to three countries this year out of 7 countries.
You need to pick 3 countries from a total of 7,
[tex]^{7} C_{3}=\frac{7!}{3!*4!} \\\\^{7} C_{3}=\frac{7*6*5*4!}{6*4!} =35[/tex]
b. The number of possibilities of arranging three digit number is,
[tex]3!=3*2=6[/tex]
c. A group of 25 people are going to run a race. The top 8 finishers advance to the finals.
you just want 8 people out of the 25 available.
the total amount of possible cases are,
[tex]^{25}C_{8}=\frac{25!}{8!*17!} =1081575[/tex]
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